End report
This commit is contained in:
parent
6a3c8cee5c
commit
9ece349d43
9 changed files with 107 additions and 61 deletions
BIN
nature/fig/U.pdf
BIN
nature/fig/U.pdf
Binary file not shown.
BIN
nature/fig/bathy2d.pdf
Normal file
BIN
nature/fig/bathy2d.pdf
Normal file
Binary file not shown.
BIN
nature/fig/pic1.jpg
Executable file
BIN
nature/fig/pic1.jpg
Executable file
Binary file not shown.
After Width: | Height: | Size: 1.8 MiB |
BIN
nature/fig/pic2.jpg
Executable file
BIN
nature/fig/pic2.jpg
Executable file
Binary file not shown.
After Width: | Height: | Size: 2.4 MiB |
BIN
nature/fig/wavelet.pdf
Normal file
BIN
nature/fig/wavelet.pdf
Normal file
Binary file not shown.
Binary file not shown.
Binary file not shown.
|
@ -119,3 +119,19 @@
|
|||
year={2020},
|
||||
publisher={Elsevier}
|
||||
}
|
||||
@book{violeau2012,
|
||||
title={Fluid mechanics and the SPH method: theory and applications},
|
||||
author={Violeau, Damien},
|
||||
year={2012},
|
||||
publisher={Oxford University Press}
|
||||
}
|
||||
@article{violeau2007,
|
||||
title={Numerical modelling of complex turbulent free-surface flows with the SPH method: an overview},
|
||||
author={Violeau, Damien and Issa, Reza},
|
||||
journal={International Journal for Numerical Methods in Fluids},
|
||||
volume={53},
|
||||
number={2},
|
||||
pages={277--304},
|
||||
year={2007},
|
||||
publisher={Wiley Online Library}
|
||||
}
|
||||
|
|
152
nature/main.tex
152
nature/main.tex
|
@ -56,47 +56,59 @@ initiation. A parametrisation of waves depending on their source is also used to
|
|||
on the type of scenario --- wave or tsunami. Those equations were later revised by \textcite{nandasena2011}, as they
|
||||
were found to be partially incorrect. A revised formulation based on the same considerations was provided.
|
||||
|
||||
The assumptions on which \citeauthor{nott2003, nandasena2011} are based were then critisized by \textcite{weiss2015}. In
|
||||
The assumptions on which \textcite{nott2003, nandasena2011} are based were then critisized by \textcite{weiss2015}. In
|
||||
fact, according to them, the initiation of movement is not sufficient to guarantee block displacement.
|
||||
\textcite{weiss2015} highlights the importance of the time dependency on block displacement. A method is proposed that
|
||||
allows to find the wave amplitude that lead to block displacement.
|
||||
allows to find the wave amplitude that lead to block displacement. Additionally, more recent research by
|
||||
\textcite{lodhi2020} has shown that the equations proposed by \textcite{nott2003, nandasena2011} tend to overestimate
|
||||
the minimum flow velocity needed to displace a block.
|
||||
|
||||
% Lack of observations -> observation
|
||||
Whether it is \textcite{nott2003}, \textcite{nandasena2011} or \textcite{weiss2015}, all the proposed analytical
|
||||
equations suffer from a major flaw; they are all based on simplified analytical models and statistical analysis.
|
||||
Unfortunately, no block displacement event seems to have been observed directly in the past.
|
||||
equations suffer from a major flaw: they are all based on very simplified analytical models and statistical analysis.
|
||||
Unfortunately, no block displacement event seems to have been observed directly in the past, and those events are
|
||||
difficult to predict.
|
||||
|
||||
In this paper, we study such an event. On February 28, 2017, a \SI{50}{\tonne} concrete block was dropped by a wave on
|
||||
the crest of the Artha breakwater. Luckily, the event was captured by a photographer, and a wave buoy located
|
||||
\SI{1.2}{\km} offshore captured the seastate. Information from the photographer allowed to establish the approximate
|
||||
time at which the block displacement occured. The goal of this paper is to model the hydrodynamic conditions near the
|
||||
breakwater that lead to the displacement of the \SI{50}{\tonne} concrete block.
|
||||
the crest of the Artha breakwater (Figure~\ref{fig:photo}). Luckily, the event was captured by a photographer, and a
|
||||
wave buoy located \SI{1.2}{\km} offshore captured the seastate. Information from the photographer allowed to establish
|
||||
the approximate time at which the block displacement occured. The goal of this paper is to model the hydrodynamic
|
||||
conditions near the breakwater that lead to the displacement of the \SI{50}{\tonne} concrete block.
|
||||
|
||||
% Modeling flow accounting for porous media
|
||||
Several approaches can be used when modelling flow near a breakwater. Depth-averaged models can be used to study the
|
||||
transformation of waves on complex bottoms. Studying the hydrodynamic conditions under the surface can be achieved using
|
||||
smoothed-particles hydrodynamics (SPH) or volume of fluid (VOF) models. SPH models rely on a Lagrangian representation
|
||||
of the fluid, while VOF models rely on an Eulerian representation. VOF models are generally more mature for the study of
|
||||
multiphase incompressible flows.
|
||||
transformation of waves on complex bottoms. Studying the hydrodynamic conditions under the surface can be achieved
|
||||
using smoothed-particles hydrodynamics (SPH) or volume of fluid (VOF) models. SPH models rely on a Lagrangian
|
||||
representation of the fluid \parencite{violeau2012}, while VOF models rely on an Eulerian representation. VOF models
|
||||
are generally more mature for the study of multiphase incompressible flows, while SPH models generally require more
|
||||
processing power for similar results \parencite{violeau2007}.
|
||||
|
||||
In this paper, we first use a one-dimensionnal depth-averaged non-linear non-hydrostatic model to verify that the signal
|
||||
measured by the wave buoy can be used as an incident wave input for the determination of hydrodynamic conditions near
|
||||
the breakwater. For this model, we use a SWASH model \parencite{zijlema2011} already calibrated by \textcite{poncet2021}
|
||||
on a domain reaching \SI{1450}{\m} offshore of the breakwater.
|
||||
In this paper, we first use a one-dimensionnal depth-averaged non-linear non-hydrostatic model to verify that the
|
||||
signal measured by the wave buoy can be used as an incident wave input for the determination of hydrodynamic conditions
|
||||
near the breakwater. For this model, we use a SWASH model \parencite{zijlema2011} already calibrated by
|
||||
\textcite{poncet2021} on a domain reaching \SI{1450}{\m} offshore of the breakwater.
|
||||
|
||||
Then, we use a nested VOF model in two vertical dimensions that uses the output from the larger scale SWASH model as
|
||||
initial and boundary conditions to obtain the hydrodynamic conditions on the breakwater. The models uses olaFlow
|
||||
initial and boundary conditions to obtain the hydrodynamic conditions on the breakwater. The model uses olaFlow
|
||||
\parencite{higuera2015}, a VOF model based on volume averaged Reynolds averaged Navier-Stokes (VARANS) equations, and
|
||||
which relies on a macroscopic representation of the porous armour of the breakwater. The model is qualitatively
|
||||
calibrated using photographs from the storm of February 28, 2017. Results from the nested models are finally compared to
|
||||
the analytical equations provided by \textcite{nandasena2011}.
|
||||
calibrated using photographs from the storm of February 28, 2017. Results from the nested models are finally compared
|
||||
to the analytical equations provided by \textcite{nandasena2011}.
|
||||
|
||||
\begin{figure*}
|
||||
\centering
|
||||
\includegraphics[height=.4\textwidth]{fig/pic1.jpg}
|
||||
\includegraphics[height=.4\textwidth]{fig/pic2.jpg}
|
||||
\caption{Photographs taken during and after the wave that displaced a \SI{50}{\tonne} concrete block onto the Artha
|
||||
breakwater.}\label{fig:photo}
|
||||
\end{figure*}
|
||||
|
||||
\section{Results}
|
||||
\subsection{Identified wave}
|
||||
|
||||
Preliminary work with the photographer allowed to identify the time at which the block displacement event happened.
|
||||
Using the data from the wave buoy located \SI{1250}{\m} offshore of the Artha breakwater, a seamingly abnormally large
|
||||
wave of \SI{14}{\m} amplitude was identified that is supposed to have lead to the block displacement.
|
||||
wave of \SI{14}{\m} amplitude was identified that is supposed to have led to the block displacement.
|
||||
|
||||
Initial analysis of the buoy data plotted in Figure~\ref{fig:wave} shows that the movement of the buoy follows two
|
||||
orbitals that correspond to an incident wave direction. These results would indicate that the identified wave is
|
||||
|
@ -115,14 +127,10 @@ with a period of over \SI{30}{\s}.
|
|||
|
||||
\subsection{Reflection analysis}
|
||||
|
||||
The results from the large scale SWASH model using two configurations --- one of them being the real bathymetry, and the
|
||||
other being a simplified bathymetry without the breakwater --- are compared in Figure~\ref{fig:swash}. The results
|
||||
obtained with both simulations show a maximum wave amplitude of \SI{13.9}{\m} for the real bathymetry, and \SI{12.1}{\m}
|
||||
in the case where the breakwater is removed.
|
||||
|
||||
The 13\% difference between those values highlights the existence of a notable amount of reflection at the buoy.
|
||||
Nonetheless, the gap between the values is still fairly small and the extreme wave identified on February 28, 2017 at
|
||||
17:23:08 could still be considered as an incident wave.
|
||||
The results from the large scale SWASH model using two configurations --- one of them being the real bathymetry, and
|
||||
the other being a simplified bathymetry without the breakwater --- are compared in Figure~\ref{fig:swash}. The results
|
||||
obtained with both simulations show a maximum wave amplitude of \SI{13.9}{\m} for the real bathymetry, and
|
||||
\SI{12.1}{\m} in the case where the breakwater is removed.
|
||||
|
||||
\begin{figure*}
|
||||
\centering
|
||||
|
@ -146,12 +154,10 @@ crest increases, with a zone reaching \SI{400}{\m} long in front of the wave whe
|
|||
qualitatively estimated position of the wave front.}\label{fig:swash_trans}
|
||||
\end{figure*}
|
||||
|
||||
\subsection{Wavelet analysis}
|
||||
|
||||
In an attempt to understand the identified wave, a wavelet analysis is conducted on raw buoy data as well as at
|
||||
different points along the SWASH model using the method proposed by \textcite{torrence1998}. The results are displayed
|
||||
in Figure~\ref{fig:wavelet} and Figure~\ref{fig:wavelet_sw}. The wavelet power spectrum shows that the major component
|
||||
in the identified wave is a high energy infragravity wave, with a period of around \SI{60}{\s}.
|
||||
in identified rogue waves is a high energy infragravity wave, with a period of around \SI{60}{\s}.
|
||||
|
||||
The SWASH model seems to indicate that the observed transformation of the wave can be characterized by a transfer of
|
||||
energy from the infragravity band to shorter waves from around \SI{600}{\m} to \SI{300}{\m}, and returning to the
|
||||
|
@ -159,8 +165,9 @@ infragravity band at \SI{200}{\m}.
|
|||
|
||||
\begin{figure*}
|
||||
\centering
|
||||
\includegraphics{fig/wavelet9312.pdf}
|
||||
\caption{Normalized wavelet power spectrum from the raw buoy timeseries.}\label{fig:wavelet}
|
||||
\includegraphics{fig/wavelet.pdf}
|
||||
\caption{Normalized wavelet power spectrum from the raw buoy timeseries for identified rogue waves on february 28,
|
||||
2017.}\label{fig:wavelet}
|
||||
\end{figure*}
|
||||
\begin{figure*}
|
||||
\centering
|
||||
|
@ -172,16 +179,17 @@ infragravity band at \SI{200}{\m}.
|
|||
|
||||
The two-dimensionnal olaFlow model near the breakwater allowed to compute the flow velocity near and on the breakwater
|
||||
during the passage of the identified wave. The results displayed in Figure~\ref{fig:U} show that the flow velocity
|
||||
reaches a maximum of \SI{14.5}{\m\per\s} towards the breakwater during the identified extreme wave. Although the maximum
|
||||
reached velocity is slightly lower than earlier shorter waves (at $t=\SI{100}{\s}$ and $t=\SI{120}{\s}$, with a maximum
|
||||
velocity of \SI{17.3}{\m\per\s}), the flow velocity remains high for twice as long as during those earlier waves. The
|
||||
tail of the identified wave also exhibits a water level over \SI{5}{\m} for over \SI{40}{\s}.
|
||||
reaches a maximum of \SI{14.5}{\m\per\s} towards the breakwater during the identified extreme wave. Although the
|
||||
maximum reached velocity is similar to earlier shorter waves, the flow velocity remains high for twice as long as
|
||||
during those earlier waves. The tail of the identified wave also exhibits a water level over \SI{5}{\m} for over
|
||||
\SI{40}{\s}.
|
||||
|
||||
\begin{figure*}
|
||||
\centering
|
||||
\includegraphics{fig/U.pdf}
|
||||
\caption{Horizontal flow velocity computed with the olaFlow model at $x=\SI{-20}{\m}$ on the breakwater armor. The
|
||||
identified wave reaches this point around $t=\SI{175}{\s}$.}\label{fig:U}
|
||||
\caption{Horizontal flow velocity computed with the olaFlow model at $x=\SI{-20}{\m}$ on the breakwater armor.
|
||||
Bottom: horizontal flow velocity at $z=\SI{5}{\m}$. The identified wave reaches this point around
|
||||
$t=\SI{175}{\s}$.}\label{fig:U}
|
||||
\end{figure*}
|
||||
|
||||
\section{Discussion}
|
||||
|
@ -194,12 +202,19 @@ twice the significant wave height over a given period. The identified wave fits
|
|||
rogue waves often occur from non-linear superposition of smaller waves. This seems to be what we observe on
|
||||
Figure~\ref{fig:wave}.
|
||||
|
||||
The wavelet power spectrum shows that a very prominent infragravity component is present, which usually corresponds to
|
||||
non-linear interactions of smaller waves. \textcite{dysthe2008} mentions that such waves in coastal waters are often the
|
||||
result of refractive focusing. On February 28, 2017, the frequency of rogue waves was found to be of 1 wave per 1627,
|
||||
which is considerably more than the excedance probability of 1 over 10\textsuperscript4 calculated by
|
||||
\textcite{dysthe2008}. Additionnal studies should be conducted to understand focusing and the formation of rogue waves
|
||||
in front of the Saint-Jean-de-Luz bay.
|
||||
As displayed in Figure~\ref{fig:wavelet}, a total of 4 rogue waves were identified on february 28, 2017 in the raw buoy
|
||||
timeseries using the wave height criteria proposed by \textcite{dysthe2008}. The wavelet power spectrum shows that a
|
||||
very prominent infragravity component is present, which usually corresponds to non-linear interactions of smaller
|
||||
waves. \textcite{dysthe2008} mentions that such waves in coastal waters are often the result of refractive focusing. On
|
||||
February 28, 2017, the frequency of rogue waves was found to be of 1 wave per 1627, which is considerably more than the
|
||||
excedance probability of 1 over 10\textsuperscript4 calculated by \textcite{dysthe2008}. Additionnal studies should be
|
||||
conducted to understand focusing and the formation of rogue waves in front of the Saint-Jean-de-Luz bay.
|
||||
|
||||
An important point to note is that rogue waves are often short-lived: their nature means that they often separate into
|
||||
shorter waves shortly after appearing. A reason for which such rogue waves can be maintained over longer distances can
|
||||
be a change from a dispersive environment such as deep water to a non-dispersive environment. The bathymetry near the
|
||||
wave buoy (Figure~\ref{fig:bathy}) shows that this might be what we observe here, as the buoy is located near a step in
|
||||
the bathymetry, from around \SI{40}{\m} to \SI{20}{\m} depth.
|
||||
|
||||
\subsection{Reflection analysis}
|
||||
|
||||
|
@ -207,10 +222,11 @@ The 13\% difference between those values highlights the existence of a notable a
|
|||
Nonetheless, the gap between the values is still fairly small and the extreme wave identified on February 28, 2017 at
|
||||
17:23:08 could still be considered as an incident wave.
|
||||
|
||||
Unfortunately, the spectrum wave generation method used by SWASH could not reproduce simlar waves to the one observed at
|
||||
the buoy. As mentionned by \textcite{dysthe2008}, such rogue waves cannot be deterministicly from the wave spectrum. For
|
||||
this reason, this study only allows us to observe the influence of reflection on short waves, while mostly ignoring
|
||||
infragravity waves.
|
||||
Unfortunately, the spectrum wave generation method used by SWASH could not reproduce simlar waves to the one observed
|
||||
at the buoy. As mentionned by \textcite{dysthe2008}, such rogue waves cannot be deterministicly from the wave spectrum.
|
||||
For this reason, this study only allows us to observe the influence of reflection on short waves, while mostly ignoring
|
||||
infragravity waves. Those results are only useful if we consider that infragravity waves behave similarly to shorter
|
||||
waves regarding reflection.
|
||||
|
||||
\subsection{Wave transformation}
|
||||
|
||||
|
@ -236,11 +252,16 @@ Those results tend to confirm recent research by \textcite{lodhi2020}, where it
|
|||
threshold tend to overestimate the minimal flow velocity needed for block movement, although further validation of the
|
||||
model that is used would be needed to confirm those findings.
|
||||
|
||||
Additionally, the flow velocity that is reached during the identified wave is not the highest that is reached in the
|
||||
model. Other shorter waves yield similar flow velocities on the breakwater, but in a smaller timeframe. The importance
|
||||
of time dependency in studying block displacement would be in accordance with research from \textcite{weiss2015}, who
|
||||
suggested that the use of time-dependent equations for block displacement would lead to a better understanding of the
|
||||
phenomenon.
|
||||
Additionally, similar flow velocities are reached in the model. Other shorter waves yield similar flow velocities on
|
||||
the breakwater, but in a smaller timeframe. The importance of time dependency in studying block displacement would be
|
||||
in accordance with research from \textcite{weiss2015}, who suggested that the use of time-dependent equations for block
|
||||
displacement would lead to a better understanding of the phenomenon.
|
||||
|
||||
Although those results are a major step in a better understanding of block displacement in coastal regions, further
|
||||
work is needed to understand in more depth the formation and propagation of infragravity waves in the near-shore
|
||||
region. Furthermore, this study was limited to a single block displacement event, and further work should be done to
|
||||
obtain more measurements and observations of such events, although their rarity and unpredictability makes this task
|
||||
difficult.
|
||||
|
||||
\section{Methods}
|
||||
|
||||
|
@ -261,14 +282,23 @@ over \SI{0.2}{\Hz}.
|
|||
|
||||
All wavelet analysis in this study is conducted using a continuous wavelet transform over a Morlet window. The wavelet
|
||||
power spectrum is normalized by the variance of the timeseries, following the method proposed by
|
||||
\textcite{torrence1998}.
|
||||
\textcite{torrence1998}. This analysis extracts a time-dependent power spectrum and allows to identify the composition
|
||||
of waves in a time-series.
|
||||
|
||||
\subsection{SWASH models}
|
||||
|
||||
\subsubsection{Domain}
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics{fig/bathy2d.pdf}
|
||||
\caption{Bathymetry in front of the Artha breakwater. The extremities of the line are the buoy and the
|
||||
breakwater.}\label{fig:bathy}
|
||||
\end{figure}
|
||||
|
||||
A \SI{1750}{\m} long domain is constructed in order to study wave reflection and wave transformation over the bottom
|
||||
from the wave buoy to the breakwater. Bathymetry with a resolution of around \SI{1}{\m} was used for most of the domain.
|
||||
from the wave buoy to the breakwater. Bathymetry with a resolution of around \SI{1}{\m} was used for most of the domain
|
||||
(Figure~\ref{fig:bathy}).
|
||||
The breakwater model used in the study is taken from \textcite{poncet2021}. A smoothed section is created and considered
|
||||
as a porous media in the model.
|
||||
|
||||
|
@ -322,12 +352,12 @@ the SWASH model, the porous armour was considered at a macroscopic scale.
|
|||
|
||||
A volume-of-fluid (VOF) model in two-vertical dimensions based on volume-averaged Reynolds-averaged Navier-Stokes
|
||||
(VARANS) equations is used (olaFlow, \cite{higuera2015}). The model was initially setup using generic values for porous
|
||||
breakwater studies. A sensibility study conducted on the porosity parameters found a minor influence of these values on
|
||||
the final results.
|
||||
breakwater studies. A sensibility study conducted on the porosity parameters found the influence of these values on
|
||||
the final results to be very minor.
|
||||
|
||||
The k-ω SST turbulence model was used, as it produced much more realistic results than the default k-ε model, especially
|
||||
compared to the photographs from the storm of February 28, 2017. The k-ε model yielded very high viscosity and thus
|
||||
strong dissipation in the entire domain, preventing an accurate wave breaking representation.
|
||||
The k-ω SST turbulence model was used, as it produced much more realistic results than the default k-ε model,
|
||||
especially compared to the photographs from the storm of February 28, 2017. The k-ε model yielded very high viscosity
|
||||
and thus strong dissipation in the entire domain, preventing an accurate wave breaking representation.
|
||||
|
||||
\subsubsection{Boundary conditions}
|
||||
|
||||
|
|
Loading…
Reference in a new issue